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Material counting technologies in numerical cognition

Periodic Reporting for period 1 - MaCoTech (Material counting technologies in numerical cognition)

Reporting period: 2018-06-15 to 2020-06-14

The rise of complex mathematical systems is seen as one of the hallmarks of civilization, if not the pinnacle of human rationality, and yet, we haven’t really understood how our innate ability to appreciate quantity, something we share with other species, yields concepts of discrete quantity, counting sequences, and simple arithmetic. Human societies vary in the degree to which their number systems become elaborated—the Western tradition has become highly complex, while some of the systems of South America, Australia, and Africa contain relatively few numbers. In the 18th century, this phenomenon was seen as a difference between “abstract” and “concrete” thinking. Even today, such preconceptions linger. They include the two systems compared for the project: the numbers of Mesopotamia, the land between the Tigris and Euphrates, and the numbers of Oceania, the region encompassing Polynesia, Micronesia, Melanesia, Papua New Guinea, and Australia. Many of these count different types of objects with object-specific numbers, misunderstood as concrete thinking.
As a cognitive archaeologist, I am interested the artifacts and behaviors used in counting, as they influence how societies organize and structure their numbers and attest to how these things were done in the past. I want to understand how artifacts and behaviors interact with the number sense and language to produce the kinds of number systems found today. I am particularly interested in how artifacts influence societal-level change in behaviors and brains to produce numeracy and literacy. Accordingly, my goals were to provide insight into our human cognitive characteristics and capabilities over the last 50,000 years and challenge historical prejudices in cross-cultural comparisons.
During the project, I gathered numerical, linguistic, geographic, temporal, and cultural data on Oceanian number systems and compared them to a similar dataset on Ancient Near Eastern numbers compiled during my earlier doctoral work. The comparison allowed me to reconstruct traditional Oceanian counting methods from ethnographic observations, experimental recreations, and algorithm formulation and analyses. The reconstruction explained numerical structure and language throughout Polynesia and solved two mysteries of several centuries’ duration: what was meant when the New Zealand indigenes were described as “counting by elevens” and why the Hawaiian word for twenty means nine and two.
Insights into why and how counting creates object-specific numbers, in turn, let me reinterpret Mesopotamian numbers, a finding presently undergoing peer review that will significantly alter how ancient numeracy is viewed. It will help dispel the outdated idea these numbers were “concrete” and highlight the importance of material forms and behaviors in counting, countering the assumption that numbers are solely mental or linguistic constructs.
I examined how Polynesian numbers changed during colonization. This yielded new insights into the way number systems elaborate generally, as associated with movements of peoples and the passage of time. I applied these insights to written notations, explaining in neurofunctional terms how and why written numbers changed as they spread across cultures and languages. I also applied these insights to other technologies and remoter periods: stone tools used two million years ago. Insights into the relation between technology, numerical structure, and conceptual content highlight the importance of materiality to human cognition. This validates a materiality-based approach to human cognition, which prioritizes the material structures used for cognitive purposes.
I disseminated (or am currently in the process of disseminating) these results in a variety of media and forums. To date, I have published four articles on the results of the project in internationally recognized, peer-reviewed journals. A fifth article is finished and under review, and four more articles are nearing completion. I authored one chapter and co-authored another for an edited anthology; I also have two chapters in press, another submitted for publication, and two more under development. I published two books during the project. The first, a revised version of my doctoral thesis, concerns the role of material devices in ancient numeracy. The second was an anthology of cognitive archaeology for which I was senior co-editor. I am currently co-editing a special journal issue. I also published two datasets in open source repositories.
I presented results from the project at eight international conferences and workshops. Two workshops were impacted by the coronavirus pandemic; these were conducted online. I attended three other international conferences, where I acted as panel moderator or expert consultant. Three planned conferences were impacted more severely; one was rescheduled to 2021, and two more did not have feasible online options. I also gave several talks at the University of Bergen, within the DICE research group, as part of the Department seminar series and annual research day, and at the SapienCE Center of Excellence. Planning for outreach talks could not be finalized because of the pandemic. I leveraged social media outlets to announce project results and publications, and I am currently contacting journalists for potential publication in non-academic venues.
I bridged evidentiary sources and types by synthesizing ethnographic and linguistic data with archaeological and textual evidence. This will have significant utility in future research and will help shift dominant paradigms in Assyriology. Neolithic numeracy is considered “concrete,” but the parallels with Polynesian “abstract” numbers suggest this interpretation is mistaken. Successfully applying contemporary data to ancient numbers may help loosen the mandate to base conclusions about Ancient Near Eastern societies solely on textual and archaeological evidence.
The project realized a novel concept: the “ephemeral abacus,” a class of impermanent counting devices that explain how two-dimensional structure (accumulation and grouping) emerges without an abacus. This result establishes an unambiguous material basis for two-dimensional structure. It shows the benefit of evaluating number systems with multidisciplinary evidence. It recategorizes traditional counting behaviors: They are no longer “primitive” strategies but are instead astute and cognitively “abstract.” Finally, it effectively counters the prevalent “internalist” model of numeracy. The insights will be applicable to number systems outside the regions and periods considered during the project.
Insight into how and why numeracy changed as it spread throughout the regions considered as case studies are more broadly applicable to the relation between technology and cognition and can be applied across significant differences in time (modern, Neolithic, Lower Paleolithic) and technology (counting devices; stone tools), demonstrating the validity of the approach.
I envision the results as having impact beyond numerical cognition. They have the potential to influence how we conceive of human thought, shifting it from an “in the head” phenomenon to one where material culture is integral. Understanding material culture as part of the human cognitive system will also give us insight into the process whereby the two change each other, a domain increasingly important to our future.
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